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Simulation tools are critical to control system development and design. Simulation of knock control systems, however, is complicated both by the stochastic nature of knock, and by the wide range of signal bandwidth and dimensionality within the feedback loop. The aim of this paper is therefore to provide a review, and in some cases an extension, of knock simulation methods from a control-oriented perspective, focusing particularly on the statistical properties of knock intensity and knock events. Deterministic notions of closed-loop performance can be misleading in this context, and recent work using Markov- and Monte-Carlo-based methods is briefly summarized as a means to obtain a more rigorous and complete description of closed-loop behavior. The methods are illustrated using a classical knock controller design.

Knock control strategies attempt to optimize the tradeoff between improving torque output and engine efficiency while also regulating knock intensity and protecting the engine from damage. This tradeoff must be made in a stochastic framework since knocking combustion behaves as a random process. This paper therefore examines the marginal and joint statistical properties of both knock intensity, and IMEP under knock limited conditions. Autocorrelation and Pearson chi-squared tests are also used to validate the cyclic independence of the data, or to identify prior cycle effects. The results and joint distribution give insight into the tri-variate relationship between knock intensity, IMEP, and spark advance, providing a foundation for improved knock/IMEP simulation and optimized controller design.

A new knock threshold optimization method is presented based on minimization of the total misclassification error of knocking / non-knocking engine operating conditions. The procedure can be used in conjunction with any knock-event-based controller, but is illustrated on a classical knock control strategy. Initial simulations suggest that the method delivers significant performance improvements with no changes other than a retuning of the controller. However, it is not possible rigorously to evaluate controller performance based on any individual experiment or simulation time history due to the random nature of the knock process. A recently developed stochastic simulation technique is therefore used to compute and compare the statistical properties of the closed loop steady state and transient response characteristics.